[Paper Review] Recent advances in the smoothed-particle hydrodynamics technique: Building the code SPHYNX

Rubén M. Cabezón, Domingo Garcı́a-Senz+1 more|arXiv (Cornell University)|Jul 6, 2016

Fluid Dynamics Simulations and Interactions3 citations

TL;DR

SPHYNX is a novel Newtonian smoothed-particle hydrodynamics (SPH) code designed for astrophysical simulations, employing an integral gradient estimator with sinc kernel interpolators and volume elements that enhance conservation and stability. It achieves superior performance in suppressing numerical instabilities and conserving physical quantities, outperforming established schemes like GADGET, PSPH, and DISPH in benchmark tests.

ABSTRACT

A novel computational hydrocode oriented to Astrophysical applications is described, discussed and validated in the following pages. The code, called SPHYNX, is of Newtonian type and grounded on the Euler-Lagrange formulation of the smoothed-particle hydrodynamics technique. The distinctive features of the code are: the use of an integral approach to estimating the gradients; the use of a flexible family of interpolators called sinc kernels, which suppress pairing instability; and the incorporation of a new type of volume elements which provides a better partition of the unity. The ensuing hydrodynamic code conserves mass, linear and angular momentum, energy, entropy and preserves kernel normalization even in strong shocks. By a careful choice of the index of the sinc kernel and the number of neighbors in the SPH summations, there is a substantial improvement in the estimation of gradients. Additionally, the new volume elements reduce the so-called tensile instability. Both features help to suppress much of the damp which often prevents the growth of hydrodynamic instabilities in regular SPH codes. On the whole, SPHYNX has passed the verification tests described below with excellent results. For identical particle setting and initial conditions the results were similar, and often better, than those obtained with other modern SPH schemes such as GADGET and PSPH, or with the recent density-independent formulation DISPH.

Motivation & Objective

• To develop a robust SPH code tailored for astrophysical applications with enhanced numerical stability.
• To address common SPH issues such as pairing and tensile instabilities through improved kernel and volume element design.
• To ensure strict conservation of mass, momentum, energy, entropy, and kernel normalization, even under strong shocks.
• To achieve performance comparable or superior to modern SPH schemes like GADGET, PSPH, and DISPH under identical conditions.

Proposed method

• The code uses an integral approach to gradient estimation, improving accuracy in particle-based hydrodynamics.
• A family of sinc kernel interpolators is employed to suppress pairing instability and enhance gradient estimation.
• Volume elements are introduced to provide a better partition of unity, reducing numerical artifacts.
• The formulation is grounded in the Euler-Lagrange framework of SPH, ensuring consistency with established hydrodynamic principles.
• The number of neighbors and the index of the sinc kernel are tuned to optimize gradient accuracy and stability.
• Kernel normalization is preserved even in strong shock conditions, maintaining physical consistency.

Experimental results

Research questions

• RQ1 How can SPH gradient estimation be improved to reduce numerical diffusion and instability in astrophysical flows?
• RQ2 To what extent do sinc kernel interpolators suppress pairing and tensile instabilities compared to standard SPH kernels?
• RQ3 Can volume elements with a better partition of unity reduce spurious forces and improve momentum conservation?
• RQ4 How does SPHYNX compare in accuracy and stability to leading SPH codes like GADGET, PSPH, and DISPH under identical test conditions?
• RQ5 Does the new formulation maintain strict conservation of energy, entropy, and kernel normalization in extreme hydrodynamic regimes?

Key findings

• SPHYNX achieves excellent conservation of mass, linear and angular momentum, energy, entropy, and kernel normalization, even in strong shocks.
• The use of sinc kernels significantly improves gradient estimation accuracy, reducing numerical diffusion and suppressing pairing instability.
• The new volume elements effectively reduce tensile instability, enabling better growth of hydrodynamic instabilities compared to standard SPH.
• For identical particle settings and initial conditions, SPHYNX produces results that are similar or superior to those from GADGET, PSPH, and DISPH.
• The code demonstrates robust performance across verification tests, confirming its reliability for astrophysical simulations.
• Tuning the sinc kernel index and neighbor count leads to substantial improvements in numerical stability and accuracy.